I think you might need to tweak the way types are determined, it seems it's weighted really heavily towards Fairy type. Myself and about 7 of my friends tried the quiz, we all got Fairy as one of our types.
This is definitely a part of it, but I also think that a lot of it is selection bias. You gotta consider the overlap of people who are really into Pokemon, and also choose to take in-depth personality quizzes - lotta Fairy-type energy in there!
Someday, when this test is common in higher academia, maybe I'll have a more accurate sense of these things...